Drogba was expected back early in January, after an op on his left knee 11 days ago. But the Ivory Coast star is worried he may now miss the African Nations Cup in Ghana from January 20 to February 10.
Chelsea had hoped Drogba would play at least one game before leaving for international duty on January 7.
But his confession could now spark a club v country row, with the Blues unwilling to risk him if he is not fit.
Drogba said: "No player would go under the knife at this crucial time if it was not serious.
"I can't say really when I'll be back.
"There's a possibility of missing the African Nations Cup."
Ivory Coast boss Uli Stieleke insisted: "Our training camp starts on January 7 and Didier will be there."